Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $$\pi$$. The difference of resultant intensities, at the point A and B, will be _____ I.

We have two light beams of intensities $$4I$$ and $$9I$$ interfering on a screen. The resultant intensity when two coherent sources of intensities $$I_1$$ and $$I_2$$ interfere with a phase difference $$\phi$$ is given by $$I_R = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$$.

At point A, the phase difference is zero ($$\phi = 0$$), so $$\cos 0 = 1$$, and the resultant intensity is $$I_A = 4I + 9I + 2\sqrt{4I \cdot 9I} = 13I + 2\sqrt{36I^2} = 13I + 12I = 25I$$.

At point B, the phase difference is $$\pi$$, so $$\cos\pi = -1$$, and the resultant intensity is $$I_B = 4I + 9I - 2\sqrt{4I \cdot 9I} = 13I - 12I = I$$.

The difference in resultant intensities is $$I_A - I_B = 25I - I = 24I$$.

Hence, the correct answer is 24.